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I have started doing option trading and as per my knowledge so far price of option rise or fall depends upon the delta (I am considering only delta for this example for brevity).

For my question I have to give an example - Lets say the stock price is $100 and its 110 CE premium is $1 with the delta of +.5. Which means that every $1 increase in the stock price will rise the option lot price by $.50. [To keep the example simple lets consider that delta is constant throughout the day even when in price is now closer to $110]

Now, assume the stock price is $105 so my 110 CE option price should be $3.5. But the price of option is just $2 because someone sold his lot at lower price.

Ex: at 1 PM option price reached $3.5 because stock price is $105 ( Option chain : ask $2 Bid $4) . But someone sold his lot at the highest ask rate (i.e. $2). So the price of option came down to $2, which ideally should be $3.5.

So, my question is that does option price really relates to stock price/delta? or it is dependent upon buyers and sellers of option?

what if the price of stock reach to $106, would option price be now $2.5 or $4? Because from $100 to $106 there is a move of $6 and ideally option lot price should be $4 ($1 + $3).

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I have started doing option trading and as per my knowledge so far price of option rise or fall depends upon the delta.

Sorry to nitpick on the wording but the price of option rise or fall does not depend upon the delta. Premium changes because of time decay, an ex-dividend date approaching, change in implied volatility, and change in carry cost. On a short term basis (intraday), the primary variables are change in IV and price. Delta is merely a statistical expectation of how much premium will change per dollar of price change in the underlying, at any given moment in time.

Ex: at 1 PM option price reached $3.5 because stock price is $105 ( Option chain : ask $2 Bid $4). But someone sold his lot at the highest ask rate (i.e. $2).

The bid is the lower price ($2) and the ask is the higher price ($4)

Option B/A spreads are very wide for illiquid options and they often become very wide when significant news is pending or it's a fast market because significant news was just released and the price of the underlying is moving quickly. In the absence of buyer and seller, the market maker widens the B/A spread defensively. There's nothing to prevent you from becoming the market (bid higher than $2 or offer at less than $4). And that is the answer to your question. The absence of participants is the reason that your option does not trade at fair market price.

If you are long the option and it trades below intrinsic value, it may be necessary for you to perform a discount arbitrage in order to realize full value (short the stock and exercise a call, or buy the stock and exercise the put) and in that order in order to avoid leg out risk.

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  • Thank you for your answer and apologies for my bad English. So, if the option price must be $3.5 but if someone sold it at the highest bid rate (assume $2) at that time, so the price of option will be $2 even though it should be $3.5 as per greeks? Absence of participant is a valid point which I ignored as of now. I should also look for IV. That's a valid point.
    – Zerotoinfinity
    Dec 4, 2019 at 23:07
  • No apology necessary. The Greeks have nothing to do with option price determination. The variables for that are stock and strike price, time remaining, dividend (if any), carry cost and volatility. Fair price doesn't mean that a fair market exists (wide bid/ask spread). Here are two useful calculators: option-price.com/index.php and ivolatility.com/calc/?ticker=SPX
    – Bob Baerker
    Dec 4, 2019 at 23:32

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